We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ-1-o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlierestimates of Peres, of Solomon and Weiss, and of Adiceam.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics